Comprehensive and Empirical Evaluation of Classical Annealing and Simulated Quantum Annealing in Approximation of Global Optima for Discrete Optimization Problems

Abstract

AbstractThe classical annealing and simulated quantum annealing are heuristic algorithms, which simulate the natural dynamics of physical systems to solve hard optimization problems. The former makes use of thermal fluctuations to arrive at the best solution, while the latter either partially or completely ignores classical dynamics and uses quantum fluctuations instead. The literature says quantum algorithms are superior to their classical counterparts in terms of convergence speed and optimal solutions. The classical effects are relatively easy to simulate on classical computing machines, but simulating quantum effects on classical machines proves hard because of their intrinsic parallel nature. To simulate quantum effects, one should make use of quantum Monte Carlo techniques borrowed from quantum physics. Most of the current literature available is focused on finding better algorithms to simulate quantum effects on classical machines, and not much research has been conducted to evaluate the performance of the existing algorithms on optimization problems. In this paper, we try to address the effectiveness of simulated quantum annealing algorithm in finding the global optima for a distinctive set of combinatorial optimization problems and also compare the solutions obtained from simulated quantum annealing with the solutions obtained from its classical counterpart, simulated annealing algorithm.KeywordsCombinatorial optimizationClassical annealingComputational complexityDiscrete optimizationEnergy landscapeGlobal optimaHamiltonianMarkov chain Monte CarloMetaheuristicsMetropolis–Hastings samplerPath integral Monte CarloPhase-space geometryQuantum annealingQuantum computingQuantum Monte CarloRate of convergenceSimulated annealingSuzuki–Trotter decompositionSimulated quantum annealingSuperpositionTunnelingThermodynamic free energy